Stability of the simultaneous processor sharing model
Abstract
We study the phenomenon of entrainment in processor sharing networks, whereby,
while individual network resources have sufficient capacity to meet demand, the
requirement for simultaneous availability of resources means that a network may
nevertheless be unstable. We show that instability occurs through a poor control
strategy, and that, for a variety of network topologies, only small modifications to
control strategies are required in order to ensure stability. For control strategies
which possess a natural monotonicity property, we give some new results for the
classification of the corresponding Markov processes, which lead to conditions both
for stability and for instability. Finally, we study the effect of variation of call size
distribution on stationary distributions and stability.